Is "Dawn Horse" a Hyrax?

Examining a Common Creationist Claim about
Hyracotherium

common creationist claim
is that Hyracotherium, which is informally called eohippus
or "dawn horse," is nothing more than a type of animal called a
hyrax. The hyraxes are a group of animals that are alive today and
are not horses. Since Hyracotherium is generally considered
to be the first "horse" the creationists conclude that this
invalidates the commonly presented series of fossils showing horse
evolution in specific and shows that evolutionists are incompetent
in general.

As you can plainly see, Hyracotherium is
not a hyrax. I would further point out that paleontologists
do know what hyraxes look like since they have described many of them
from the fossil record, often in the same books where they describe fossil
horses. For reference, one can find images of modern horse skulls
here
and
here
while images of more fossil horses can be found
here.

Creationists sometimes mention that Sir Richard Owen, the man who first described
a Hyracotherium fossil, named it after a hyrax in 1841 as if this
justified their conclusion. Stephen Jay
Gould3
wrote about Owen's naming of Hyracotherium:

He did not recognize its relationship with horses (he considered this animal, as
his chosen name implies, to be a possible relative of hyraxes, a small group of
Afro-Asian mammals, the "coneys" of the Bible). In this original
article, Owen likened his fossil to a hare in one passage and to something
between a hog and a hyrax in another....

Thus I really don't think that Owen's naming of the creature was really
that strong a thing
to lean on in the first place. (And of course the creationists could have
tried to find a picture of a hyrax skull themselves.)

"This creature has a skeleton very similar to that of Eohippus
yet it has not 'evolved' to what the present day horses
are. If evolution were true Eohippus, nor anything like it, should
[not] be found today." The second sentence shows author
falsely thinks evolution is a linear progression.

"...probable that Eohippus [sic] is really an
extinct variety of hyrax..."

There is a variant version of this
claim. Lawrence O. Richards4
wrote:

Today no evolutionist thinks that the "short-necked
creatures not much bigger than a domestic cat" is related to the
modern horse at all. The fossil called Eohippus, or Dawn
Horse, is now considered to be a close relative of the rock rabbit!

The hyrax, which creationists usually claim that
Hyracotherium is, has now been transformed into a
rock rabbit (click here to see a skull)!
"rEvolutionary Thinking Where Do We Come From Really?
A Critical Analysis of the Scientific Evidence for
Evolution"
(the "rEvolutionary" is not
a typo) copies large portions of what Richards wrote including
the section in question.
A different
page
on the same web site claims it is
"indistinguishable" from a hyrax. So we have a web site
that claims Hyracotherium is a rabbit on one page and a
hyrax on another!
A dentist by the name of Wm. T.
Greenshaw
repeats
the claim by plagiarizing Richards via
verbatim copying without giving credit whatsoever. The Richards
book received the
Gold Medallion Book Award "in recognition of excellence
in evangelical Christian literature."
John N. Moore of the
Creation Research Society
is listed as a consulting editor. And yet the book is just
incredibly inaccurate. Richards falsely claims that some evolutionists
think that a reptile laid an egg that hatched into a fully developed
bird and illustrates the claim with a picture of a bird hatching from an
egg laid by a dinosaur though the creature illustrated is a mammal-like
reptile. Richards falsely claims that hemoglobin is "exactly the
same" in all species with it. In reality the hemoglobin
of different species is different unless extremely closely related
and these differences can be used to
trace
the course of evolution though today DNA data is used more often.
Richards falsely claims that carbon-14 decays into carbon-12 when
in reality it decays into nitrogen-14 via beta decay. This book
has many other errors like this.